10C survey of radio sources at 15.7 GHz - II. First results
Davies, M.L.; Franzen, T.M.O.; Waldram, E.M.; Grainge, K.J.B.; Hobson, M.P.; Hurley- Walker, N.; ... ; Zwart, J.T.L.
Citation
Davies, M. L., Franzen, T. M. O., Waldram, E. M., Grainge, K. J. B., Hobson, M. P., Hurley- Walker, N., … Zwart, J. T. L. (2011). 10C survey of radio sources at 15.7 GHz - II. First results. Monthly Notices Of The Royal Astronomical Society, 415(3), 2708-2722.
doi:10.1111/j.1365-2966.2011.18925.x
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License: Leiden University Non-exclusive license Downloaded from: https://hdl.handle.net/1887/59592
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10C survey of radio sources at 15.7 GHz – II. First results
AMI Consortium: Matthew L. Davies,
1† Thomas M. O. Franzen,
1† Elizabeth M. Waldram,
1Keith J. B. Grainge,
1,2Michael P. Hobson,
1Natasha Hurley-Walker,
1Anthony Lasenby,
1,2Malak Olamaie,
1Guy G. Pooley,
1Julia M. Riley,
1Carmen Rodr´ıguez-Gonz´alvez,
1Richard D. E. Saunders,
1,2Anna M. M. Scaife,
3Michel P. Schammel,
1Paul F. Scott,
1Timothy W. Shimwell,
1David J. Titterington
1and Jonathan T. L. Zwart
41Astrophysics Group, Cavendish Laboratory, 19 J. J. Thomson Avenue, Cambridge CB3 0HE
2Kavli Institute for Cosmology Cambridge, Madingley Road, Cambridge CB3 0HA
3Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2, Ireland
4Columbia Astrophysics Laboratory, Columbia University, 550 West 120th Street, New York, NY 10027, USA
Accepted 2011 April 15. Received 2011 April 12; in original form 2010 December 15
A B S T R A C T
In a previous paper (Paper I), the observational, mapping and source-extraction techniques used for the Tenth Cambridge (10C) Survey of Radio Sources were described. Here, the first results from the survey, carried out using the Arcminute Microkelvin Imager Large Array (LA) at an observing frequency of 15.7 GHz, are presented. The survey fields cover an area of≈27 deg2to a flux-density completeness of 1 mJy. Results for some deeper areas, covering
≈12 deg2, wholly contained within the total areas and complete to 0.5 mJy, are also presented.
The completeness for both areas is estimated to be at least 93 per cent. The 10C survey is the deepest radio survey of any significant extent (0.2 deg2) above 1.4 GHz.
The 10C source catalogue contains 1897 entries and is available online. The source catalogue has been combined with that of the Ninth Cambridge Survey to calculate the 15.7-GHz source counts. A broken power law is found to provide a good parametrization of the differential count between 0.5 mJy and 1 Jy. The measured source count has been compared with that predicted by de Zotti et al. – the model is found to display good agreement with the data at the highest flux densities. However, over the entire flux-density range of the measured count (0.5 mJy to 1 Jy), the model is found to underpredict the integrated count by≈30 per cent.
Entries from the source catalogue have been matched with those contained in the catalogues of the NRAO VLA Sky Survey and the Faint Images of the Radio Sky at Twenty-cm survey (both of which have observing frequencies of 1.4 GHz). This matching provides evidence for a shift in the typical 1.4-GHz spectral index to 15.7-GHz spectral index of the 15.7-GHz- selected source population with decreasing flux density towards sub-mJy levels – the spectra tend to become less steep.
Automated methods for detecting extended sources, developed in Paper I, have been applied to the data;≈5 per cent of the sources are found to be extended relative to the LA-synthesized beam of ≈30 arcsec. Investigations using higher resolution data showed that most of the genuinely extended sources at 15.7 GHz are classical doubles, although some nearby galaxies and twin-jet sources were also identified.
Key words: catalogues – surveys – radio continuum: galaxies – radio continuum: general.
We request that any reference to this paper cites ‘AMI Consortium: Davies et al. 2011’.
†E-mail: m.davies@mrao.cam.ac.uk (MLD); t.franzen@mrao.cam.ac.uk (TMOF)
1 I N T R O D U C T I O N
1.1 Background
The Ninth Cambridge (9C) Survey of Radio Sources (Waldram et al. 2003, 2010), carried out using the Ryle Telescope (RT) at an
observing frequency of 15.2 GHz, was a milestone in the exploration of the high-radio-frequency sky, as the first survey of significant ex- tent and depth at such a high radio frequency. Since the publication of the first 9C paper, extensive survey work has been carried out using the Australia Telescope Compact Array at 20 GHz (ATCA;
Ricci et al. 2004; Sadler et al. 2006; Massardi et al. 2008, 2011;
Murphy et al. 2010). The two surveys are complementary, with the 9C survey probing deeper flux-density levels (down to 5.5 mJy) and the ATCA surveys covering shallower and wider areas (most recently, the whole southern sky).
It is well known that high-frequency radio surveys are highly time-consuming. The scaling of interferometer primary-beam areas with frequency (∝ν−2) and the typical synchrotron spectra of radio sources (∝ν−0.7) conspire so that the time required to carry out a survey of equivalent depth and sky coverage, using a telescope of a fixed aperture diameter, scales asν3.4. Things are somewhat better if it is assumed that the available bandwidth scales linearly with frequency. However, the fact that the noise temperatures of the available front-end, low-noise amplifiers used in interferometers tend to increase with frequency must also be taken into account.
For these reasons, relatively little survey work has been under- taken at high radio frequencies and the knowledge of the source population remains poor. Nevertheless, the familiarity with the properties of this population is important for the interpretation of the results from observations of the cosmic microwave background (CMB), such as those made by Planck (Tauber et al. 2010). At mm wavelengths, foreground radio sources are the dominant source of the contamination of small-scale CMB anisotropies (de Zotti et al.
1999). Waldram et al. (2003, 2010) have demonstrated that the ex- trapolation of the flux densities of sources at low frequencies can- not be relied upon to predict their high-frequency properties, which emphasizes the value of survey work at the frequencies of interest (10 GHz) for CMB work.
Samples of bright sources selected at high radio frequencies have significant proportions with flat or rising spectra (see e.g. Taylor et al. 2001; AMI Consortium: Davies et al. 2009). These sources are mainly believed to be blazars with synchrotron self-absorbed spectra; the self-absorbed components of such sources are often highly variable (see e.g. AMI Consortium: Franzen et al. 2009).
High-frequency-selected samples also include appreciable num- bers of sources with convex spectra, peaking at GHz frequencies (see e.g. Bolton et al. 2004). Some of these GHz peaked spectrum (GPS) sources (see O’Dea 1998, for a review) are believed to be associated with young objects, which later expand into powerful radio sources, though many are dominated by the emission from a strongly beamed self-absorbed component (Bolton et al. 2006). Sur- veys such as the 9C survey provide flux-density-limited samples, which are useful for gaining further understanding of the evolution of such objects.
1.2 This work
Since the 9C survey was carried out, the RT has been transformed, by the installation of new front-end receivers and back-end electronics (including a new correlator), into the Arcminute Microkelvin Im- ager (AMI) Large Array (LA) (see AMI Consortium: Zwart et al.
2008, for a detailed description of the telescope). The LA is a radio synthesis telescope located≈19 m above the sea level near Cam- bridge. It is used to observe at a centre frequency of 15.7 GHz and has a usable bandwidth of 4.5 GHz. At this frequency, the tele- scope has a full width at half-maximum (FWHM) primary beam of
≈5.5 arcmin and a resolution of ≈30 arcsec.
The LA has been used to carry out the Tenth Cambridge (10C) Survey of Radio Sources. As part of this survey, the improved flux sensitivity of the LA, compared with the RT, has been used to explore the 15-GHz-band sky to sub-mJy levels. In a previous paper (AMI Consortium: Franzen et al. 2011, hereinafter Paper I), detailed technical information regarding the survey strategy, mapping and source-extraction techniques for the 10C survey was provided. In this paper, the first results from 10 fields, including the 15.7-GHz source count, are presented. Throughout this paper, any equatorial coordinates use equinox J2000 and spectral indices are defined using the convention that S∝ ν−α.
2 T H E 1 0 C S O U R C E C ATA L O G U E
The techniques used for observing, mapping and source extraction are fully described in Paper I. The fields, the positions of which are given in Section 3, were surveyed using a ‘rastering’ technique, with observations being carried out between 2008 August and 2010 June.
Each field was observed using a set of telescope pointing directions spaced at 4.0 arcmin intervals and lying on a 2D hexagonally gridded lattice, projected on to the plane of the sky. A raster map that combines the individualCLEANed maps belonging to each of the pointing directions was produced for each field; the raster map for one of the survey fields is shown in Fig. 1. In addition, a noise map that shows how the noise varies across the raster map was created for each field; these noise maps are used in identifying sources, as described in Paper I.
Information about the sources was extracted from the raster maps, using a combination of in-house software and tasks belonging to the
AIPS,1for the inclusion in the 10C source catalogue. Source finding was carried out using a flux-density threshold of 4.62σ ; the reason for this slightly unusual choice is explained in Sections 2.1 and 2.2.
In Section 3, areas within each of the survey fields, bounded by lines of constant right ascension (RA) and declination (Dec.), complete to flux densities of 1.0 and 0.5 mJy, are defined. A short section of the catalogue is shown in Table 1. The methods used to extract various parameters are fully described in Paper I; the final column indicates which of the areas (see Section 3) each of the sources lies within. The complete source list, which contains 1897 entries, is available online (see Supporting Information), along with an explanatory readme file. This information can also be found on the survey website (http://www.mrao.cam.ac.uk/surveys/10C), where it is also planned to make theFITSmaps for each of the survey fields publicly available, once further 10C observations have been completed.
Individual positional error estimates have not been assigned to each source. The positional errors in both RA and Dec. for a source detected at the 5σ level, in any of the survey fields, are estimated to be 3–4 arcsec; this range reflects the fact that the synthesized beam is slightly elliptical and has dimensions which vary with field declination. The assessment of the source positional accuracy was made using simulations in which point sources were inserted into the map of one of the survey fields; the extracted source positions were compared with the nominal values.
The results of the simulation were found to agree well with the positional errors that would be expected from theory, taking into account Gaussian thermal noise. Higher resolution follow-up observations are required to assess the positional accuracy for the brighter sources. Only the highest-flux-density source in the 10C
1Astronomical Image Processing System – http://www.aips.nrao.edu
Figure 1. The raster map of one of the 10C survey fields (J0024+3152). The map was produced by combining approximately 1000 individual constituent maps, weighted according to their rms noise; the individual maps wereCLEANed before being combined. The area of lower noise at the centre of the raster map is clearly visible.
survey catalogue has a counterpart in the catalogue of the Jodrell Bank-VLA Astrometric Survey (Patnaik et al. 1992; Browne et al.
1998; Wilkinson et al. 1998). The measured positions of this source agree within 3.5 arcsec.
There were some problems with the analysis and mapping of the 10C survey data that required some adaptations to the source-finding procedure described in Paper I. These adaptations are described in the remainder of this section.
2.1 Checking the flux-density scale
As a check of the raster maps’ flux-density scale,≈50 of the bright- est sources detected in the maps were selected for pointed follow-up observations, carried out during 2010 June and August using the LA.
To avoid complicating the analysis, only sources that showed no ev- idence of extension in the raster maps were selected. The data from these observations were mapped using the sameCLEANing scheme as used for the raster maps, but phase self-calibration was also applied.
Fig. 2 shows the peak flux densities for each of the sources mea- sured using the raster and (self-calibrated) pointed maps. The figure indicates that the flux densities of the sources measured from the raster maps are systematically low compared with those from the self-calibrated pointed observations. However, because the pointed
follow-up observations were carried out about 2 yr after the com- mencement of the raster observations, it is important to consider the effect of source variability on this result.
Fig. 2 indicates that the pointed flux density of one source is almost twice its raster flux density; this difference is almost certainly attributable to genuine flux-density variability. Having said this, the number of genuinely variable sources within the sample is likely to be small. The sources selected for pointed follow-up have flux densities ranging between approximately 10 and 40 mJy. Results from Waldram et al. (2010) indicate that 15-GHz-selected samples containing sources with flux densities in this range are likely to be dominated by steep-spectrum sources, which do not ordinarily display significant variability.
Nevertheless, the median percentage difference has been used to quantify the discrepancy between the pointed and raster flux densities because it is less sensitive to genuine source variability than the mean, the value of which could be strongly affected by a small number of highly-variable sources within the sample. The median percentage difference between the pointed and raster flux densities was calculated to be 8.2 per cent with an uncertainty in this value of≈2 per cent.
Since a number of the 10C survey fields overlap with areas mapped as part of the 9C survey, as an additional check, the flux
Table1.Samplesfromthe10Csourcecatalogue,whichisavailableinfullonlinewithanexplanatoryreadmefile(seeSupportingInformation).[Thisinformationcanalsobefoundonthesurveywebsite (www.mrao.cam.ac.uk/surveys/10C),whereitisalsoplannedtomaketheFITSmapsforeachofthesurveyfieldspubliclyavailable,oncefurther10Cobservationshavebeencompleted.]Theextractionprocedures forthevariousparametersarefullydescribedinPaperI.Thecolumnsarethesourcename;thegroupname,whichindicatesoverlappingsources(thegroupisnamedafterthesourcewiththehighestpeakflux densityinthegroupandthenumberofobjectsinthegroupisgiveninbrackets);RA,αpk(J2000),andDec.,δpk(J2000),ofthesourcepeak;thepeakfluxdensity,Spk,anditsuncertainty,δSpk;RA,αin,andDec., δin,ofthesourcecentroid(J2000;relevantforextendedsources);theintegratedfluxdensity,Sin,anditsuncertainty,δSin;thecriticalvalue,ecrit,ofthemajor-axis,abovewhichthesourceisdefinedasextended, havingdeconvolvedthetelescope’spoint-sourceresponsefromthefitted2DGaussian;thelengths,emajandemin,ofthemajor-axisandminor-axisandpositionangle,eθ,ofthesourceafterthedeconvolution– theeminandeθcolumnsareleftblankforsourcesclassifiedaspointlike;thesourcetype,t–pointlike(P)orextended(E);aflag,‘*’,indicatingthattheerrorfromtheapproximationofthepoint-sourceresponse issignificantand,consequently,theresultsfromtheGaussianfittingoughttobetreatedwithcaution;andtheregionofthesurveyinwhichthesourcefalls–deep(D),shallow(S)orneither(N).Notethatthe parametersfromtheGaussianfittingareomittedifthefittingdidnotconverge. SourcenameGroupnameαpkδpkSpkδSpkαinδinSinδSinecritemajemineθtFR (mJy)(mJy)(mJy)(mJy)(arcsec)(arcsec)(arcsec)(◦)le ag gi o n 10CJ002129+32270000:21:29.8+32:27:0024.691.3400:21:29.9+32:27:0123.271.2825.013.5P*S 10CJ002215+31492300:22:15.8+31:49:230.510.0700:22:15.8+31:49:250.400.0943.20.0PD 10CJ002215+32170700:22:15.8+32:17:071.550.1000:22:15.8+32:17:071.470.1325.09.5PD 10CJ002216+31515300:22:16.2+31:51:530.640.0700:22:16.2+31:51:520.560.1039.10.0PD 10CJ002219+31471700:22:19.3+31:47:170.830.0800:22:19.3+31:47:190.760.1134.211.9PD 10CJ002220+32353710CJ002222+323549(2)00:22:20.0+32:35:372.150.2000:22:19.4+32:35:313.510.4432.558.20.049.7ES 10CJ002221+31442200:22:21.9+31:44:220.670.0700:22:22.0+31:44:210.610.1036.30.0PD 10CJ002222+32280300:22:22.1+32:28:030.770.1500:22:22.0+32:28:040.770.2452.39.4PS 10CJ002222+32354910CJ002222+323549(2)00:22:22.3+32:35:492.400.2100:22:22.8+32:35:513.170.4030.944.90.041.7ES 10CJ002223+31250910CJ002224+312409(3)00:22:23.3+31:25:091.460.1000:22:23.4+31:25:101.360.1225.05.3PD 10CJ002224+31362700:22:24.4+31:36:270.620.0600:22:24.4+31:36:290.740.1135.531.9PD 10CJ002224+31240910CJ002224+312409(3)00:22:24.9+31:24:096.860.3700:22:24.9+31:24:107.140.4025.09.1PD 10CJ002227+31252010CJ002224+312409(3)00:22:27.4+31:25:200.660.0700:22:27.3+31:25:190.590.1036.54.3PD 10CJ002232+31521300:22:32.1+31:52:130.440.0700:22:32.1+31:52:150.560.1347.833.7PD 10CJ002233+32380200:22:33.4+32:38:021.040.1800:22:33.6+32:38:020.970.2747.97.6PS 10CJ002237+31091000:22:37.7+31:09:101.500.1700:22:37.6+31:09:111.510.2740.717.2PS 10CJ002238+31262200:22:38.6+31:26:220.880.0800:22:38.7+31:26:230.840.1131.07.1PD 10CJ002240+31450300:22:40.1+31:45:030.410.0700:22:40.0+31:45:000.510.1347.944.9PD 10CJ002241+31000700:22:41.3+31:00:071.340.2000:22:41.3+31:00:061.330.3349.716.7PS 10CJ002241+31170400:22:41.3+31:17:040.890.1400:22:41.2+31:17:040.920.2349.215.9PS 10CJ002242+31184400:22:42.3+31:18:440.840.1100:22:42.2+31:18:431.280.2440.943.70.00.2ES 10CJ002246+31311300:22:46.0+31:31:133.330.1900:22:45.8+31:31:165.220.3125.042.99.0145.3ED 10CJ002246+32061400:22:46.1+32:06:140.470.0700:22:46.2+32:06:150.400.1043.811.6PD 10CJ002249+31033600:22:49.3+31:03:362.820.2100:22:49.4+31:03:372.960.3029.410.9PS 10CJ002251+32230500:22:51.3+32:23:050.500.0800:22:51.3+32:23:060.390.1045.70.0PD 10CJ002252+32020400:22:52.7+32:02:040.460.0500:22:52.7+32:02:060.520.0937.127.6PD
Figure 2. The peak flux densities of≈50 sources as measured from the raster maps and from maps created using self-calibrated data from pointed follow-up observations. Points lying on the line represent sources having identical flux densities when measured using the raster and pointed maps.
densities measured from the pointed observations were compared with the values measured from pointed 9C observations. Having corrected the phase errors in the 10C pointed observations using self-calibration, there was found to be good agreement between the 9C and 10C pointed values with a median percentage difference of<1 per cent – the median is again used for the same reason as given above. It is noted that, owing to the small difference in the observing frequencies and the typical spectra of radio sources, the 10C flux densities might be expected to be slightly lower than the 9C values – this was, in fact, the case.
Data from a large number of observations, carried out during a range of weather conditions, were combined to create the raster maps; whereas the data used to produce the pointed maps were collected during single, short observations during relatively good (dry) observing conditions. As a result, the weather conditions dur- ing the pointed observations may not be typical of those during the raster observations. However, in practice, data collected during periods of poor weather are either omitted entirely or significantly downweighted with respect to data collected during good weather conditions.
A modulated noise signal, injected at the front end of each an- tenna, was monitored throughout the raster observations. The data were then weighted, on a sample-by-sample basis, according to the value of the ‘rain gauge’ – that is the ratio of the power of the mod- ulated noise signal to the total power input to the correlator (which is kept constant) to that obtained in cool, dry, clear weather condi- tions. In addition, data for which the rain gauge was less than 50 per cent (this is rather a conservative criterion) were omitted. This is because the amplitude correction applied to the data becomes unre- liable during heavy rain, as no attempt to account for atmospheric absorption is made in applying this correction.
Atmospheric-related phase effects are not thought to make any significant contribution to the phase errors present in the data.
During LA observations, a phase-calibrator source is observed
for 1 min at 10 min intervals. Even using the telescope’s longest (110-m) baseline, the measured phase varies only slowly on time- scales much longer than 10 min. If the measured phase for a cal- ibrator source does change by more than 30◦ between successive visits to the source, the affected data are automatically omitted dur- ing the data-reduction stage; however, such a large phase difference between successive calibrator visits is observed only very rarely.
Similarly, any data for which the estimated error in the measured phase of the calibrator is>15◦are also omitted automatically.
The discrepancy between the flux densities measured using the phase-self-calibrated pointed observations and the raster observa- tions is instead attributed to phase errors in AMI data resulting from the uneven spacings of the time-delays in the telescope’s lag corre- lator. Holler et al. (2007) explain this problem in detail and propose a solution. In practice, however, further work is required to analyse the data from the correlator correctly.
2.2 Correcting the sources’ flux densities for phase errors Unfortunately, the great majority of the sources in the 10C raster maps are detected with an insufficient signal-to-noise ratio (S/N) to allow self-calibration to be successfully applied to the data. There- fore, a correction to the source flux densities based on the difference between the flux densities measured from the raster maps and the self-calibrated pointed maps is applied; as a final step in the source- finding procedure, all source flux densities are multiplied by 1.082 before their inclusion in the 10C catalogue.
The uncertainties in the flux densities are increased to take ac- count of this scaling and the uncertainty in the correction factor (≈2 per cent), which is in any case small compared with the esti- mated LA calibration uncertainty of 5 per cent. As in Paper I, the uncertainty in an uncorrected peak flux density, S, is taken to be
σn2+ (0.05S)2, whereσnis the thermal noise at the source posi- tion, estimated from the noise map. The uncertainty in the corrected value is therefore
1.082S
σn2+ (0.05S)2
S2 + 0.022. (1)
Initially, it was intended to carry out source finding at 5σ ; since, assuming Gaussian statistics for the map noise, such a scheme would result in a highly reliable catalogue with ≈0.1 false detections.
Further, the completeness of such a catalogue would have been very high (94 per cent) at 0.5 and 1 mJy in the deep and shallow regions, respectively. However, owing to the effect of phase errors, a source of S= 1 mJy falling within the shallow area of the survey, which ought to be detected at≥5σ , will only be detected at ≥5σ /1.082 = 4.62σ .
Therefore, in order to achieve the desired high levels of com- pleteness at 0.5 and 1 mJy, it was decided to carry out the source finding at 4.62σ . The catalogue completeness is fully discussed in Section 4. The slight relaxation in the source-finding criterion is likely to have only a small adverse effect on the reliability of the catalogue. Assuming Gaussian statistics for the map noise, and given the number of synthesized beam areas in the survey maps, it is estimated that about one source in the final catalogue will be a false positive.
2.3 Excluding areas around bright sources
The 10C raster maps often display an increased level of noise around bright (15 mJy) sources. This is attributable to amplitude, phase and deconvolution errors in the data. The elevated noise level close
to bright sources is generally not fully reflected by the noise maps, because the noise is highly non-Gaussian in these regions. There- fore, such detections close to sources of S> 15 mJy were auto- matically excluded from the final source catalogue. In addition, detections close to a number of fainter sources (the faintest being
≈9 mJy) were also excluded manually from the final catalogue after inspecting the maps.
Empirically, the area of the elevated noise around each bright source (the ‘exclusion zone’), from which the source detections were rejected, was found to be well represented by a circle, centred on the source position, of radius
re= 12
Spk/mJy 250
1/2
arcmin, (2)
where Spkis the peak flux density of the source. Table 2 shows the centre coordinates and radii of the exclusion zones applied to the survey data.
The dynamic range of the LA – that is the ratio of a source’s peak flux density to the flux density of the brightest artefact in a map close to the source – is≈50:1. The brightest source detected in the 10C survey is≈270 mJy. A conservative approach, which also serves to simplify the completeness areas for the construction of the source count, has been taken by assuming that sources with S≥ 9 mJy can be detected anywhere in the total areas. In contrast, any putative source with a peak flux density less than this value that falls within the exclusion zone of a bright source is not included in the final 10C source catalogue. Thus, the area used for calculating the source counts for sources with S< 9 mJy does not include the exclusion zones around bright sources. The total area excluded from around bright sources is 0.6 deg2.
3 S U RV E Y F I E L D S
The 10C survey fields are centred at J0024+3152, J0259+2610, J0734+5432, J0824+6931, J0939+3115, J1046+5904, J1052+5730, J1524+4321, J1543+4420 and J1733+4148.
Fig. 3 shows the positions of these fields, which were chosen to be widely spread in RA and away from the Galactic plane. For each field, areas complete to 1.0 and 0.5 mJy (apart from the exclusion zones) have been defined by selecting those areas in which the noise,σn, estimated using the relevant noise map is 0.1≤ σn <
0.2 mJy andσn < 0.1 mJy, respectively. Over a large portion of the areas, the estimated noise is significantly lower than the upper bounds and therefore the completeness is close to 100 per cent for both regions at their nominal completeness levels.
The areas complete to 0.5 mJy are entirely contained within the areas complete to 1.0 mJy and are referred to as the ‘deep’ regions.
Areas of higher noise, complete to 1.0 mJy, but excluding the deep regions, are referred to as the ‘shallow’ areas. Fig. 4 shows the deep and shallow regions for one of the fields. The survey catalogue in- cludes a flag for each source, indicating whether it falls in the deep (D) or shallow (S) areas. Sources that fall outside these regions al- together (i.e. in areas of higher noise towards the edges of the raster maps) are indicated by ‘N’. For a source with evidence of extension, the flag is based on the source’s centroid position; otherwise, the peak position is used. The ‘total’ areas are those areas complete to 1 mJy but not excluding the deep regions – in other words, the com- bined deep and shallow areas. The lines of RA and Dec. bounding the total and deep areas, for each of the fields, are given in Tables 3 and 4, respectively.
Table 2. The centre positions of the exclusion zones around bright sources and their radii.
RA Dec. Radius (arcmin)
00:20:50.4 +31:52:29 3.39 00:21:29.8 +32:26:60 3.63 00:23:09.9 +31:14:01 4.26 00:26:06.2 +32:08:33 2.83 00:28:10.7 +31:03:46 3.85 00:29:20.4 +32:16:55 3.17 00:29:33.1 +32:44:58 4.45 02:59:55.1 +26:27:26 2.31 03:01:05.5 +25:47:16 2.92 03:01:37.3 +25:41:54 3.04 07:31:17.4 +53:38:58 4.25 07:36:52.9 +54:29:17 2.70 08:18:16.1 +69:16:53 4.06 08:23:02.5 +69:14:20 2.94 09:35:59.5 +31:27:27 3.17 09:36:36.9 +32:03:35 3.31 09:37:06.2 +32:06:58 5.41 09:41:03.2 +31:26:14 3.30 09:41:46.2 +31:55:03 3.05 09:42:08.8 +32:06:42 3.48 10:47:19.3 +58:21:14 4.93 10:49:40.0 +58:35:31 3.35 10:50:07.1 +56:53:37 3.38 10:50:54.0 +58:32:33 3.50 10:51:41.4 +59:13:08 3.80 10:52:25.4 +57:55:08 3.46 10:52:54.5 +59:22:18 3.56 10:54:26.9 +57:36:48 3.69 15:20:41.6 +44:13:18 3.43 15:21:49.4 +43:36:37 12.51 15:27:51.8 +43:52:05 2.85 15:28:19.8 +42:33:35 4.01 15:40:33.5 +44:34:01 3.32 15:41:10.0 +44:56:34 4.58 15:42:23.1 +43:59:15 3.81 15:46:04.5 +44:49:14 3.02 17:25:34.5 +41:53:03 4.33 17:27:49.3 +42:21:40 4.45 17:29:01.9 +41:40:04 2.68 17:30:41.6 +41:02:58 6.14 17:31:23.7 +41:01:38 3.01 17:37:59.6 +41:54:51 5.00 17:38:35.4 +42:21:43 3.08 17:40:08.9 +41:36:09 6.31 17:40:17.2 +42:14:30 2.93 17:40:52.1 +42:34:47 5.79
4 C O M P L E T E N E S S
4.1 Simulations
Simulations were carried out to investigate the completeness of the survey. A number of realizations were used (12 for the deep areas and 13 for the shallow) in which 250 equal-flux-density, simulated point sources were inserted into the raster map of J0024+3152.
The flux density of the simulated sources was different for each of the realizations. The positions of the simulated sources were chosen randomly but were not altered between realizations; to avoid the simulated sources affecting each other, it was insisted that no simulated source could lie within 2 arcmin of any other. Sources were not inserted in the exclusion zones around bright sources,
Figure 3. The positions of the 10C survey fields, shown using an equatorial- plane projection with the North Pole at the centre. The declination circles are at intervals of 10◦and the Galactic plane is indicated by the thick black line.
Figure 4. The shallow (lighter shading) and deep areas belonging to J0024+5432.
since, as explained above, the completeness limit is expected to be much higher for these areas compared with the remainder of the maps. In order to investigate the completeness as a function of flux density, the flux density of the sources was changed between realizations.
For each realization, the ordinary source-finding procedures were applied to the map and the proportion of simulated sources that were recovered was calculated for the shallow and deep areas. Three of the simulated sources were found to lie too close to real sources to be detected separately. In these cases, the simulated source was considered to be detected if the recovered source position was closer to the simulated rather than the real source position.
Fig. 5 shows the proportion of sources detected for each of the realizations compared with the expected detection rate, which is calculated for a particular region of the map as follows. For a specific
source flux density, the probability of detection can be calculated at the position of each pixel by taking account of the value of the noise map at that position and by using Gaussian statistics. The probability of detection over the whole region is straightforwardly calculated by averaging over pixels.
The plots show that, in general, there is good agreement between the predicted completeness curves and the results of the simula- tion. However, for the fainter sources, the detection rate is slightly higher than predicted, whilst the converse is true for the brighter sources. Source confusion is likely to be responsible for these re- sults. A number of the highest flux-density simulated sources, that would otherwise have been detected, were not recovered owing to their proximity to real, bright sources. This effect prevented the completeness from reaching 100 per cent as quickly as predicted. At fainter flux densities, however, the opposite effect, whereby a source is boosted in flux density owing to its proximity to a real, fainter source, so that it is unexpectedly detected, becomes important.
The peak flux densities of sources detected with low S/Ns are typically biased slightly high, because the peak position tends to be coincident with a positive noise fluctuation. This is an additional factor serving to boost the detection rate at low S/Ns. The presence of this effect was confirmed by extracting the flux densities of the sources at the precise positions with which they were simulated;
the values were found to be systematically low compared with the extracted peak flux densities and were found to reflect better the simulated flux densities.
4.2 Using the noise maps to estimate the completeness Having established by simulation that, assuming Gaussian statistics for the noise, the noise maps can be used to provide reasonable estimates of the survey completeness, the noise maps from all the fields were used to estimate the completeness of the 10C survey. The probability of a source with the true flux density ˆS being included in the survey catalogue when located on a pixel with a corresponding noise-map value ofσnwas taken, according to Gaussian statistics, to be
P ( ˆS ≥ 4.62σn)=
∞
4.62σn
1 2πσn2
exp−
x − ˆS/1.0822
2σn2 dx. (3) In carrying out this calculation, the fact that sources are detected with flux densities lower than their true values has been taken into account by including the factor of 1/1.082.
Knowing the actual distribution of noise-map pixel values, equa- tion (3) can be used to estimate the completeness, as a function of flux density, for the shallow and deep regions of the survey; Fig. 6 shows these estimates for both areas. For the shallow regions, the catalogue is estimated to be≈94 per cent complete by 1 mJy and 99 per cent complete by≈1.16 mJy. For the deep areas, the catalogue is estimated to be≈93 per cent complete by 0.5 mJy and 99 per cent complete by≈0.61 mJy.
5 S O U R C E C O U N T S
The 15.7-GHz differential source counts have been calculated by binning the sources from the final catalogue according to their peak flux densities, except for those that display evidence of being ex- tended relative to the telescope-synthesized beam (this is the case for 5.5 per cent of sources), for which integrated flux densities were used.
The binned differential-source-count data are given in Table 5.
For the highest flux-density bin, data from the entirety of the total ar- eas have been used. The bins for sources with flux densities between
Table 3. The areas complete to 1 mJy.
Field RA range Dec. range Area (deg2)
J0024+3152 00:19:54.2 to 00:29:38.3 +31:00:04 to +32:43:05 3.56 J0259+2610 02:56:43.6 to 03:02:32.8 +25:19:17 to +27:02:17 2.24 J0734+5432 07:30:02.8 to 07:38:50.7 +53:41:42 to +55:23:07 2.16 J0824+6931 08:17:08.6 to 08:31:23.8 +68:41:04 to +70:22:41 2.11 J0939+3115 09:36:22.1 to 09:42:25.9 +30:24:22 to +32:06:18 2.20 J1046+5904 10:39:25.5 to 10:52:31.2 +58:13:12 to +59:55:07 2.86 J1052+5730 10:47:36.8 to 10:57:21.3 +56:48:56 to +58:10:22 1.78 J1524+4321 15:20:10.7 to 15:29:24.6 +42:30:20 to +44:11:21 2.83 J1543+4420 15:38:30.5 to 15:47:46.6 +43:28:43 to +45:11:13 2.83 J1733+4148 17:25:37.0 to 17:41:01.3 +40:57:34 to +42:40:06 4.90
Table 4. The areas complete to 0.5 mJy. Note that there are three deep regions associated with J0259+2610.
Field RA range Dec. range Area (deg2)
J0024+3152 00:20:59.1 to 00:28:27.1 +31:19:38 to +32:23:29 1.69 J0259+2610 02:57:50.5 to 03:01:24.1 +25:38:31 to +26:43:51 0.87 02:56:50.2 to 02:57:50.5 +25:53:05 to +26:28:22 0.13 03:01:24.1 to 03:02:31.4 +25:53:05 to +26:28:22 0.15 J0734+5432 07:31:47.0 to 07:37:06.6 +54:00:59 to +55:04:59 0.82 J0824+6931 08:19:21.5 to 08:29:26.1 +68:57:47 to +70:07:19 1.02 J0939+3115 09:37:32.8 to 09:41:15.9 +30:42:52 to +31:47:13 0.85 J1046+5904 10:41:30.0 to 10:50:24.5 +58:32:47 to +59:35:08 1.19 J1052+5730 10:49:57.7 to 10:55:32.7 +57:08:03 to +57:51:28 0.54 J1524+4321 15:21:32.3 to 15:27:57.3 +42:50:56 to +43:52:21 1.19 J1543+4420 15:39:51.6 to 15:46:21.3 +43:49:49 to +44:50:48 1.18 J1733+4148 17:26:44.0 to 17:39:49.8 +41:17:01 to +42:19:40 2.54
Figure 5. Results of a simulation to investigate the completeness of the survey. The filled circles show the proportion of the simulated sources recovered as a function of flux density within the deep (σn≤ 0.1 mJy) area of J0024+3152. The solid line shows the completeness predicted based on the noise-map pixel values, assuming Gaussian statistics for the noise. The open squares and dashed line show the results for the shallow (0.1< σn≤ 0.2 mJy) area.
1 and 9 mJy include sources from the total regions but exclude the areas around bright sources given in Table 2. The bins for sources with flux densities between 0.5 and 1 mJy include sources from the deep regions (again excluding areas around bright sources). The source count is not calculated for S> 25 mJy, since it is biased low
Figure 6. The estimated probability of detection for the shallow (dashed line) and deep (solid line) areas of all survey fields. The dot–dashed horizon- tal line indicates a probability of 1. The dot–dashed vertical lines indicate the 0.5- and 1.0-mJy nominal completeness limits for the deep and shallow areas, respectively.
in this flux-density range; using 9C data, several of the fields were selected to contain as few sources with S> 25 mJy as possible.
At 0.5 mJy, the completeness limit of the deep areas, the sur- vey is limited by thermal rather than confusion noise. Above this
Table 5. Data for the 10C source count.
Bin start Bin end Number of Area S (mJy) S (mJy) sources (deg2)
9.000 25.000 46 27.46
5.500 9.000 51 26.86
2.900 5.500 142 26.86
2.050 2.900 135 26.86
1.500 2.050 148 26.86
1.250 1.500 113 26.86
1.000 1.250 160 26.86
0.900 1.000 36 11.96
0.775 0.900 56 11.96
0.680 0.775 51 11.96
0.600 0.680 64 11.96
0.540 0.600 61 11.96
0.500 0.540 46 11.96
flux-density level, it is estimated that there are typically 170 LA- synthesized beam areas per source.
The effect of the calibration errors of≈5 per cent is negligible, serving to boost the number of sources in each bin by 1 per cent (owing to the sign of the slope of the source count). However, the bias (Eddington 1913) due to the thermal noise will play a more important role for the bins at the faintest flux-density levels. Given the slope of the counts and the noise properties of the deep region, the number of sources in the faintest flux-density bin is expected to be boosted by≈7 per cent. However, this effect is almost exactly balanced by the small degree of incompleteness that affects these faintest flux-density bins. Consequently, no corrections for the effect of Eddington bias or incompleteness have been applied.
The 10C differential source count is shown in Fig. 7. As in all subsequent plots showing source counts, Poisson errors, on the number of sources in each bin, are indicated for each of the points and the bars parallel to the flux-density axis represent the bin widths, not error bars.
Figure 7. The 10C differential source count. Poisson errors, on the number of sources in each bin, are indicated for each of the points. The bars parallel to the flux-density axis represent the bin widths, not error bars. The fitted broken-power-law count is indicated by the solid line.
Figure 8. Differential source counts from the shallow and deep regions of the 10C survey. The fitted 10C source count is indicated by the solid line.
An attempt was made to fit a single power law to the data. How- ever, such a model did not appear to fit the data well. Consequently, a broken power law has been fitted to the data. A method was used whereby the sum of the squared differences between the measured and predicted areas under the curve, over all bins, was minimized. In carrying out the minimization, the points were weighted according to their respective Poisson errors. The positions of the points in the S direction within the bins have been plotted, in Fig. 7, on the basis of the fitted exponents to reflect the ‘centre of gravity’ of each bin.
The fitted differential source count is
n(S) ≡dN dS ≈
⎧⎪
⎪⎨
⎪⎪
⎩ 24
S Jy
−2.27
Jy−1sr−1for 2.8 ≤ S ≤ 25 mJy
376 S
Jy
−1.80
Jy−1sr−1for 0.5 ≤ S < 2.8 mJy.
Tests were carried out to check that the broken-power-law model does indeed provide an improved fit to the data, compared with the single-power-law model. An F-test indicated that the null hypothesis – that the data are more likely to have been drawn from the simpler model – can be rejected at>99.9 per cent confidence. A comparison of the models using Akaike’s information criterion was similarly emphatic, indicating that the broken-power-law model is≈1000 times more likely to be correct than the simpler model.
In order to check the self-consistency of the source count, the data were used to construct separate counts for the shallow and deep regions. Fig. 8 shows the counts from the two regions over- laid. The deep counts are derived from an area amounting to 11.96 deg2(except for the highest flux-density bin, which contains data from 12.19 deg2). The shallow counts use data from 14.90 deg2 (15.27 deg2for the highest flux-density point). The plot shows good agreement, within the uncertainties, between the counts derived from the two regions over the common flux-density range.
5.1 Adding in data from the 9C survey
It is possible to extend the 10C source count to higher flux densities by the inclusion of data from the 9C survey. It is also possible
to improve the source count statistics between 5.5 and 25 mJy by including 9C data, since the 9C survey contains regions that are complete over this flux-density range. There is a small difference in the observing frequencies of the 9C (15.2 GHz) and 10C surveys (15.7 GHz). Therefore, in combining the data sets, the source flux densities from the 9C survey catalogue have been corrected to take into account this difference. The correction was made by assuming a typical spectral index between 15.2 and 15.7 GHz that varies as a function of source flux density.
The assumed flux-density-dependent spectral index is indicated in Fig. 9. The correction was calculated by fitting a logarithmic function to the points in the plot. For each of the three lowest flux- density points (indicated by the filled squares), the median flux density versus the median value of the 1.4- to 15.2-GHz spectral index,α151.4.2, of sources, with flux densities in the relevant ranges, detected as part of the 9C survey (see table 9 of Waldram et al. 2010) has been plotted. For the highest flux-density point (indicated by the filled triangle), the median flux density versus median value ofα3316, measured by AMI Consortium: Davies et al. (2009), for sources belonging to a flux-density-limited source sample (L´opez-Caniego et al. 2007) from the 3-yr Wilkinson Microwave Anisotropy Probe (WMAP) data has been plotted. The number of sources belonging to the samples represented by these points ranges between 84 and 381.
For both the 9C and WMAP samples, it has simply been assumed that the spectral indices can be extended over the small additional frequency ranges to 15.7 GHz (from 15.2 GHz in the case of the 9C samples and from 16 GHz for the WMAP sample). The approach followed is admittedly not perfect, particularly since the sample for
Figure 9. The filled squares represent the median 1.4- to 15.2-GHz spectral indices for complete 15.2-GHz-selected source samples from the 9C survey.
The filled triangle represents the median 16- to 33-GHz spectral index for a complete 33-GHz-selected sample from the WMAP 3-yr data. The dashed line indicates the assumed typical spectral index, as a function of flux density, used to make corrections to the flux densities of individual 9C sources, to account for the small difference in the observing frequencies of the 9C and 10C surveys. This allowed the 10C source count to be extended to flux densities>25 mJy by the inclusion of 9C data. The typical spectral index was calculated by fitting a logarithmic function to the data points.
the highest flux-density point was selected at 33 GHz. Nevertheless, because the difference in observing frequencies between the surveys is very small, the corrections are similarly small (at most a few per cent) and the method is considered acceptable.
Fig. 10 shows the combined 9C and 10C differential source count.
Data from areas of the 9C survey presented in Waldram et al. (2003) and Waldram et al. (2010) have been used in constructing the count.
The data used for each bin are shown in Table 6. For the intermediate flux-density ranges, for which there are data from both surveys, some of the 9C survey data were excluded. This was to avoid double counting the areas that were surveyed as part of both the 9C and 10C surveys.
Using the same method as described above, a broken power law was fitted to the binned differential count. As previously, a broken power law was found to be a significantly better fit to the data than a single power law. Again, an F-test indicated that the null hypothesis – that the data are more likely to have been drawn from the simpler model – can be rejected at>99.9 per cent confidence. The best- fitting broken-power-law parametrization of the source count is
n(S) ≡dN dS ≈
⎧⎪
⎪⎨
⎪⎪
⎩ 48
S Jy
−2.13
Jy−1sr−1for 2.2 mJy ≤ S ≤ 1 Jy
340 S
Jy
−1.81
Jy−1sr−1for 0.5 ≤ S < 2.2 mJy.
This fitted count is found to give a good fit to the data, with a reduced chi-squared value of 0.75. The probability of obtaining a reduced chi-squared value greater than 0.75 by chance, given the number (20) of degrees of freedom, is 78 per cent. The fit is indicated in Fig. 10.
5.2 Comparison with the de Zotti model
In Fig. 11, the combined 9C and 10C source count is compared with the latest version of the 15-GHz source-count model by de Zotti et al. (2005), extracted from their website2on 2011 March 1;
for completeness, the model counts, over the relevant flux-density range, are provided in Appendix A. No attempt has been made to correct for the small frequency difference between the measured and model source counts but this is likely to make little difference to the overall conclusions.
The model count is in good agreement with the measured count at the high-flux-density end. However, the shape of the plotted model count is somewhat different from that of the measured count; so that, with decreasing flux density, the model first overpredicts and then, below≈5 mJy, underpredicts the measured count.
The total number of sources per steradian with flux densities between 0.5 mJy and 1 Jy, predicted by the model, was calculated by integrating the model differential source count between these limiting flux densities. Since the predicted counts are given at a number of discrete flux densities (see Table A1), the integration was carried out piecewise by approximating the model count as a power law between successive pairs of points.
The number of sources per unit area predicted by the model was found to be only 70 per cent of the measured value. Because the differential count is largest at the low-flux-density end, the underprediction of the count at the lowest flux densities dominates over the overprediction at slightly higher flux densities, explaining the 30 per cent deficit over the entire range.
2http://web.oapd.inaf.it/rstools/srccnt/srccnt_tables
Figure 10. The combined 9C and 10C 15.7-GHz differential source count. Different symbols are used to distinguish between the areas that were used to derive the count for the various flux-density bins: ‘9C1’ indicates areas presented in Waldram et al. (2003); ‘9C2’ refers to areas presented in Waldram et al. (2010);
and ‘10C’ is used to designate areas presented in this paper. The fitted count is indicated by the solid line.
Table 6. Data for the combined 9C and 10C source counts.
Bin start Bin end Number of Area S (mJy) S (mJy) sources (deg2)
500.000 1000.000 8 520.00
200.000 500.000 27 520.00
100.000 200.000 47 520.00
60.000 100.000 92 520.00
40.000 60.000 97 520.00
30.000 40.000 99 520.00
25.000 30.000 79 520.00
16.000 25.000 62 124.60
12.000 16.000 64 124.60
10.000 12.000 48 124.60
9.000 10.000 15 47.83
6.400 9.000 48 47.23
5.500 6.400 44 47.23
2.900 5.500 142 26.86
2.050 2.900 135 26.86
1.500 2.050 148 26.86
1.200 1.500 140 26.86
1.000 1.200 133 26.86
0.900 1.000 36 11.96
0.775 0.900 56 11.96
0.680 0.775 51 11.96
0.600 0.680 64 11.96
0.540 0.600 61 11.96
0.500 0.540 46 11.96
Figure 11. The normalized (S2.5 dNdS) combined 9C and 10C differential source count. The symbols indicating the areas from which the counts were derived are identical to those in Fig. 10. The fitted broken-power- law parametrization is indicated by the solid line. The dashed line indicates the prediction of the latest version of the de Zotti et al. (2005) model.
